Hi, Kevin, and welcome to the BrickWood forum.
We’re not in the business of breaking hearts, though I suspect yours might crack just a bit.
So, if your build resembles the photo in this link…yes, you need some insulation between the firebrick in the arch and the stucco.
Now, to avoid a complete break: you do not have to remove all the stucco, just the area over the exposed arch brick and the chimney. Since you did not use chicken wire, it’s going to come off pretty easily. Your best bet is to trace a line in pencil that follows the line of the inside arch (four inches from the inside edge) on the stucco, then take your mason’s chisel and gently tap to separate that stucco from the shell that covers the insulation. (I am presuming you used chicken wire under that. If you did not, we have a larger conversation to follow.)
Once arch and chimney front are exposed, and presuming you do want to cover them completely in stucco (and I do like that look), you can lay in a single layer of insulation. Scrap pieces from the main job would be fine. And if it helps, you can use dots of adhesive to tack them in place on this vertical surface, but don’t go overboard with it. Follow that with chicken wire, then new layers of stucco.
Alternate thought: if you think you’d rather close off the front of the oven (see the Mattone Barile instructions for details), then don’t bother with any of this. Follow the instructions for closing it off, apply insulation and chicken wire, then finish with stucco.
I do feel your pain on this, Kevin, but that stucco as it sits is guaranteed to crack and look nasty as soon as your curing fires progress to the real thing. Good luck and let us know how it turns out!